This invention relates to the processing and synthesizing of complex signals, and more specifically relates to a novel method and apparatus for processing and identifying the components of a complex signal and for synthesizing complex signals in which signal components are identified in terms of discrete locations in a one or more dimensional representation, derived from the measurement and/or generation of at least the epoch and damping of the signal components which make up the complex waveform which is being processed or produced.
The analysis and synthesizing of complex waveforms is a well developed art and has application to a large number of fields. For example, the analysis of acoustical signals having complex waveforms produced by one or more spaced sources is well known. Similarly, analysis of signal waveforms of electrical signals, seismic signals and other signals is well known with application in speech processing, environmental sensing, biomedical signal analysis, and the like. Equivalent systems are known for the generation of complex waveforms as may be encountered in fields such as music synthesizing, the production of artificial speech, and the like.
In presently known acoustical systems, it is possible to obtain desired information from only simple waveforms and from single source objects, such as a single speaker against a low background noise. The effect of factors such as amplitude, dynamic range, enunciation and sex of the speaker will cause complexity and unacceptable performance in speech analysis equipment. Similar problems exist in waveform analysis of signals produced by sources other than the human voice. Those systems which do exist are relatively costly and use substantial input power for their operation due to complex structure and complex processing algorithms.
Virtually all existing complex signal analysis systems are based on some form of Fourier or spectral analysis or, more generally, on the use of least-squares estimation of polynomial functions. Such methods have a common deficiency in that during the processing sequence, important information is lost due to the need for a relatively long measurement interval required to estimate the polynomial coefficients of a Fourier series. Since the measuring interval must be relatively long, the measurement process loses information related to "epoch" which relates to the time at which a new individual signal within the waveform has begun. Because of this restriction, Fourier type analysis technique cannot identify multiple source objects which occur simultaneously within the interval of observation or measurement of a complex waveform produced by the multiple objects.
If, in a spectral analysis system, the interval for estimation of the polynomial coefficients is reduced in order to improve epoch accuracy, then the accuracy of the mean square estimate of the source function is reduced. Consequently, in the case of Fourier analysis, the spectrum becomes more and more blurred as the sampling window is reduced in time.
The difficulties of present systems for analysis of stochastic signals are summarized by a known time-frequency uncertainty which specifies that accuracy in a frequency domain requires low resolution in the time domain and vice-versa. This is described, for example, in the article by D. Gabor entitled "Theory of Communication", Journal of IEEE, Volume 39, Part III, No. 26, November, 1946. The above problem is also described by S. M. Kay and S. L. Marple, "Spectrum Analysis - A Modern Perspective", IEEE Proceedings, Volume 69, November, 1981, pp. 1380-1419 and by H. Bremerman, "Pattern Recognition, Functions and Entropy", IEEE, Transactions on Biomedical Engineering, Volume BME-15, No. 3, July, 1968.
It is interesting to note that the human ear has solved the waveform analysis problem, although the operation of the ear in this analysis function is not understood. In older theoretical analyses of the operation of the ear, it was assumed that the hearing process employs spectral processing. Thus, an early theoretical model of hearing was made by Von Helmholtz in 1863. The Von Helmholtz model was based on a Fourier or frequency domain signal analysis. Both Von Helmholtz and his successors concentrated on studying well-defined and relatively simple signal conditions, especially with only one signal at a time. These simplifications have provided a reasonable basis for a theoretical study, but disregard how the ear deals with frequency discrimination over a wide, logarithmic range, how it responds to transients and its ability to detect and identify sounds over a wide amplitude and dynamic range with near optimum detection sensitivity and how it can discriminate multiple sources spatially and temporally even when they are interleaved with wide ranges in amplitude. Acoustic sources can also be identified by the ear in spite of background noise and extreme distortion of amplitude and phase. This is the well known "cocktail party effect" in which the human ear can pick out the voice of an unseen speaker from a background of other voices of equal or greater amplitude. The use of Fourier analysis type techniques fails to explain many of the functions of the human ear, including those described above, in terms of a consistent signal processing theory.
Signal processing methods and apparatus which are presently available are extremely complex and expensive, even though their functions do not come close to the efficiency and wide range application of the human ear. The present invention provides signal processing which more nearly approaches the results obtained by the human ear and which is less complex and costly than presently available equipment.